Meson multiplicities needed for the construction of the hadronic cocktail were obtained from fitting transverse momentum spectra of various mesons with a modified Tsallis function (right panel of Fig. REF ).
The respective multiplicities vary little within systematic uncertainties compared to numbers extracted from the same data using the original Tsallis distribution [1]}.
Cross sections were derived by multiplying the fully corrected and integrated differential multiplicity distributions with the total inelastic cross section taken to be \(\sigma ^{\mathrm {p}\,\mathrm {p}}_{\mathrm {inel.}} = 42\)  mb.
The differential cross section for \(\eta \)  and \(\omega \)  production were obtained from hadronic and photon decay channels in the similar way.
For unobserved phase space regions \(m_t\)  scaling was assumed to hold and all cross sections to be constant in the measured \(\Delta \eta \)  bin (boost invariance).
The cross sections parameterized in that way were input to the PHENIX decay generator used to derive the respective dielectron yields (hadronic cocktail).
The meson decay generator (EXODUS) uses mass dependent eTFF's for the meson Dalitz decays and samples angular distributions of electrons w.r.t.  the virtual-photon axis as explained in Sec. REF .
For the two-body decay no polarization of vector mesons and partial decay widths \(\Gamma _{\mathrm {e}^+\mathrm {e}^-}\)  given by VDM with finite width corrections calculated by Gounaris [2]} are assumed.
The \(\rho \)  production is assumed to proceed via pion-pion-annihilation and hence a cut-off in the meson mass distribution towards \(2 m_{\pi }\)  appears.
The measured transverse momentum distributions of dielectrons, shown in the middle panel of Fig. REF  for various invariant mass bins, are well described by the cocktail calculation based on the meson production cross sections derived as described above and shown as full lines.
